Taylor series and adaptive passivity-based control for conical tanks level regulation

This manuscript proposes using a finite Taylor series (TS) and normalized adaptive passivity-based control (NAPBC) for nonlinear systems encompassing the level regulation of conical tanks. TS-NAPBC is as effective and robust as the traditional proportional integer control, and NAPBC. However, these latest techniques assume the existence of the input–output dynamical model obtained after computing a coordinates transformation of the original state-space representation, which takes time and is problematic. In contrast, the proposed TS-NAPNC exceeds them by having a faster and more straightforward design and commissioning, avoiding an input–output transformation, and not needing to know the plant parameters value. The TS-NAPBC deals with the unknown parameters and control direction of the TS. Moreover, it has adaptive law modifications due to the presence of a time-varying parameter associated with the TS rest term. The second Lyapunov stability method and Barbalat Lemma theoretically validate the proposition. Comparative experimental results show the effectiveness of TS-NAPBC and its robustness in front of plant parameter variations.